(a) The derivative of a function (b) The definite integral 3. Find the antiderivative: 1 x...
1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate F(2) F(2) = (c) Evaluate F(1) F(1) = (d) Calculate the definite integral 3x + 5) dx = 2. Calculate the definite integral. Give exact answers. Зе -Te du (a) Find an antiderivative F(*) = (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (d) Calculate the definite integral.
Part 3: The derivative of a definite integral and the chain rule Suppose dt. Use the Fundamental of Theorem of Calculus to calculate 9 +t / Suppose F(x) = f* (510) dt. Use the Fundamental of Theorem of Calculus to calculate on (F(x?). (F(x)) = C
Objective The usual procedure for evaluating a definite integral is to find the antiderivative of the integrand and apply the Fundamental Theorem of Calculus. However, if an antiderivative of the integrand cannot be found, then we must settle for a numerical approximation of the integral. The objective of this project is to illustrate the Trapezoidal Rule and Simpson's Rule. Description To get started, read the section 8.6 in the text. In this project we will illustrate and compare Riemann sum,...
help please Evaluate the definite integral using the Fundamental Theorem of Calculus. (1+ (1 + 14х5) dx Use The Fundamental Theorem of Calculus and the antiderivative found in Step 2 to evaluate the definite integral. fo* (2 + 14x5) dx = = (x+3x0916 (1+](O* )-( O*+O) “) 10 3
solve 1 and 2. Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B) cos (x3) A) 6x5 cos (x3) Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B)...
Using part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (b) f(x) = بدايه dt (c) 3x+1 f(x) = st sin(+4) dt
1. Find the derivative of the function y (x) , showing all steps used 2. Find the derivative of the function y(x)In x), showing all steps used. 3. Show that sin(x) 1- (sin(x) cot (x))2, showing all steps 4. Evaluate the following integral:珓 1-cos' (x) cos(x) dx, showing all steps. 5. If the rate at which a car's position is changing is given by the formula0.3t2 - 2.0t +100, where x is in meters and t is in seconds, find...
Name(PRINT): MAC 2233 Worksheet 10 1. Calculate the definite integral. % (223 -3. + 5) dx (a) Find an antiderivative F() (b) Evaluate F(2) F(2) (c) Evaluate F(1) F(1) = (d) Calculate the definite integral. (23- - 3.r+5) da 2. Calculate the definito integral. Give exact answers. 3e="é do (a) Find an antiderivative F() (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (a) Calculate the definite integral. 3e
F) 3w-5 w-25 (2) Which of the following definite integrals cannot be evaluated using the Fundamental Theorem of Calculus? (This has nothing to do with being able to find an antiderivative), D) S B) sin() In(x) dx (C) x tan(x) dx A) dr dx 1+e In(x2 +1) dx sin(® dx\ (G) J V+ sin H) F) 2 dx o )u xb [(x)1-(x)ul, 3 x+1dx be evaluated using the FTOC ? C) F) 3w-5 w-25 (2) Which of the following definite...
Using part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 11. (21 points) Using part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (a) f(x) = [ 71 – dt (b) $(a) = Sie a